Parallelism in Manipulator Dynamics. Revision.
MASSACHUSETTS INST OF TECH CAMBRIDGE ARTIFICIAL INTELLIGENCE LAB
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This paper addresses the problem of efficiently computing the motor torques required to drive a lower-pair kinematic chain e.g., a typical manipulator arm in free motion, or a mechanical leg in the swing phase given the desired trajectory. i.e., the Inverse Dynamics problem. It investigates the high degree of parallelism inherent in the computations, and presents two mathematically exact formulations especially suited to high-speed, highly parallel implementations using special-purpose hardware or VLSI devices. In principle, the formulations should permit the calculations to run at speed bounded only by IO. The first presented is a parallel version of the recent linear Newton-Euler recursive algorithm. The time cost is also linear in the number of joints, but the real-time coefficients are reduced by almost two orders of magnitude. The second formulation reports a new parallel algorithm which shows that it is possible to improve upon the linear time dependency. The real time required to perform the calculations increases only as the log 2 of the number of joints. Either formulation is susceptible to a systolic pipelined architecture in which complete sets of joint torques emerge at successive intervals of four floating-point operations. Hardware requirements necessary to support the algorithm are considered and found not to be excessive, and a VLSI implementation architecture is suggested. We indicate possible applications to incorporating dynamical considerations into trajectory planning, e.g. it may be possible to build an on-line trajectory optimizer. Author
- Theoretical Mathematics